A157430 Primes of the form 9*(p^4)-2 or 9*(p^4)+2, arising in Paley-Hadamard difference sets.

727, 5623, 21611, 131771, 751691, 8311687, 16867447, 25431851, 71014331, 109056251, 350550731, 3170478247, 4435959611, 4678970407, 6353205851, 9659548091, 11977770247, 26525659687, 29365277771, 39262233611, 52986054967

Offset

1,1

Comments

Polhill is able to construct Paley-Hadamard difference sets of the Stanton-Sprott family in groups of the form (Z_3)^2 X (Z_p)^4t X (Z_(9p^4t)+2 or -2 when 9*(p^4t)-2 or 9*(p^4t)+2 is a prime power. In this sequence, we are taking just the t=1 case, a prime power as first power of prime.

References

John Bowen Polhill, Paley partial difference sets in groups with order not a prime power, 1046th Meeting of the AMS, Washington, DC, January 5-8, 2009.

Links

Table of n, a(n) for n=1..21.

Example

a(1) = 9*(3^4) - 2 = 727 is prime. a(2) = 9*(5^4) - 2 = 5623 is prime. a(3) = 9*(7^4) + 2 = 21611. a(4) = 9*(11^4) + 2 = 131771. a(5) = 9*(17^4) + 2 = 751691. a(6) = 9*(31^4) - 2 = 8311687. a(7) = 9*(37^4) - 2 = 16867447. a(8) = 9*(41^4) + 2 = 25431851.

Crossrefs

Sequence in context: A129117 A158394 A038600 * A215158 A178654 A094733

Adjacent sequences: A157427 A157428 A157429 * A157431 A157432 A157433

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 01 2009

Extensions

More terms from R. J. Mathar, Mar 06 2009

Status

approved